Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-8x-2y &= 6 \\ -3x-2y &= -9\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $1$ $\begin{align*}8x+2y &= -6\\ -3x-2y &= -9\end{align*}$ Add the top and bottom equations. $5x = -15$ Divide both sides by $5$ and reduce as necessary. $x = -3$ Substitute $-3$ for $x$ in the top equation. $-8( -3)-2y = 6$ $24-2y = 6$ $-2y = -18$ $y = 9$ The solution is $\enspace x = -3, \enspace y = 9$.